From minimal Higgs inflation with $$(R^2)$$ term in palatini gravity to Swampland conjectures under ACT constraints

Abstract In this work, we explore the viability of minimal Higgs inflation with $$(R^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> term in Palatini gravity within the framework of the swampland program. Our analysis focuses on three central conjectures: the Further Refined de Sitter Swampland Conjecture (FRDSSC), the Scalar Weak Gravity Conjecture (SWGC), and the Strong Scalar Weak Gravity Conjecture (SSWGC). By examining theoretical predictions alongside observational constraints, we investigate how the free parameters of the model influence its consistency with these conjectures. The results demonstrate that the model remains compatible with the FRDSSC across a broad parameter space and aligns well with recent data from the Atacama Cosmology Telescope (ACT), reinforcing its standing as a promising inflationary scenario. A detailed study of the SWGC and SSWGC further reveals that the model’s compatibility is highly sensitive to variations in the scalar coupling parameter. A threshold behavior is identified, above which the parameter space supporting consistency expands significantly. Moreover, the SSWGC exhibits a wider region of validity compared to the SWGC, highlighting the stronger conjecture’s broader applicability. Taken together, these findings confirm that minimal Higgs inflation with $$(R^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> term in Palatini gravity is consistent with multiple swampland criteria and possesses robustness under parameter variations.